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Modern Multivariate Statistical Techniques Regression, Classification, and Manifold Learning

ISBN-10: 0387781889
ISBN-13: 9780387781884
Edition: 2008
List price: $99.00
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Book details

List price: $99.00
Copyright year: 2008
Publisher: Springer
Publication date: 3/11/2013
Binding: Hardcover
Pages: 733
Size: 6.50" wide x 9.75" long x 1.50" tall
Weight: 3.124
Language: English

Preface
Introduction and Preview
Multivariate Analysis
Data Mining
From EDA to Data Mining
What Is Data Mining?
Knowledge Discovery
Machine Learning
How Does a Machine Learn?
Prediction Accuracy
Generalization
Generalization Error
Overfitting
Overview of Chapters
Bibliographical Notes
Data and Databases
Introduction
Examples
Example: DNA Microarray Data
Example: Mixtures of Polyaromatic Hydrocarbons
Example: Face Recognition
Databases
Data Types
Trends in Data Storage
Databases on the Internet
Database Management
Elements of Database Systems
Structured Query Language (SQL)
OLTP Databases
Integrating Distributed Databases
Data Warehousing
Decision Support Systems and OLAP
Statistical Packages and DBMSs
Data Quality Problems
Data Inconsistencies
Outliers
Missing Data
More Variables than Observations
The Curse of Dimensionality
Bibliographical Notes
Exercises
Random Vectors and Matrices
Introduction
Vectors and Matrices
Notation
Basic Matrix Operations
Vectoring and Kronecker Products
Eigenanalysis for Square Matrices
Functions of Matrices
Singular-Value Decomposition
Generalized Inverses
Matrix Norms
Condition Numbers for Matrices
Eigenvalue Inequalities
Matrix Calculus
Random Vectors
Multivariate Moments
Multivariate Gaussian Distribution
Conditional Gaussian Distributions
Random Matrices
Wishart Distribution
Maximum Likelihood Estimation for the Gaussian
Joint Distribution of Sample Mean and Sample Covariance Matrix
Admissibility
James-Stein Estimator of the Mean Vector
Bibliographical Notes
Exercises
Nonparametric Density Estimation
Introduction
Example: Coronary Heart Disease
Statistical Properties of Density Estimators
Unbiasedness
Consistency
Bona Fide Density Estimators
The Histogram
The Histogram as an ML Estimator
Asymptotics
Estimating Bin Width
Multivariate Histograms
Maximum Penalized Likelihood
Kernel Density Estimation
Choice of Kernel
Asymptotics
Example: 1872 Hidalgo Postage Stamps of Mexico
Estimating the Window Width
Projection Pursuit Density Estimation
The PPDE Paradigm
Projection Indexes
Assessing Multimodality
Bibliographical Notes
Exercises
Model Assessment and Selection in Multiple Regression
Introduction
The Regression Function and Least Squares
Random A Case
Fixed A Case
Example: Bodyfat Data
Prediction Accuracy and Model Assessment
Random-X Case
Fixed- X Case
Estimating Prediction Error
Apparent Error Rate
Cross-Validation
Bootstrap
Instability of LS Estimates
Biased Regression Methods
Example: PET Yarns and NIR Spectra
Principal Components Regression
Partial Least Squares Regression
Ridge Regression
Variable Selection
Stepwise Methods
All Possible Subsets
Criticisms of Variable Selection Methods
Regularized Regression
Least Angle Regression
The Forwards Stagewise Algorithm
The LARS Algorithm
Bibliographical Notes
Exercises
Multivariate Regression
Introduction
The Fixed-X Case
Classical Multivariate Regression Model
Example: Norwegian Paper Quality
Separate and Multivariate Ridge Regressions
Linear Constraints on the Regression Coefficients
The Random-X Case
Classical Multivariate Regression Model
Multivariate Reduced-Rank Regression
Example: Chemical Composition of Tobacco
Assessing the Effective Dimensionality
Example: Mixtures of Polyaromatic Hydrocarbons
Software Packages
Bibliographical Notes
Exercises
Linear Dimensionality Reduction
Introduction
Principal Component Analysis
Example: The Nutritional Value of Food
Population Principal Components
Least-Squares Optimality of PCA
PCA as a Variance-Maximization Technique
Sample Principal Components
How Many Principal Components to Retain?
Graphical Displays
Example: Face Recognition Using Eigenfaces
Invariance and Scaling
Example: Pen-Based Handwritten Digit Recognition
Functional PCA
What Can Be Gained from Using PCA?
Canonical Variate and Correlation Analysis
Canonical Variates and Canonical Correlations
Example: COMBO-17 Galaxy Photometric Catalogue
Least-Squares Optimality of CVA
Relationship of CVA to RRR
CVA as a Correlation-Maximization Technique
Sample Estimates
Invariance
How Many Pairs of Canonical Variates to Retain?
Projection Pursuit
Projection Indexes
Optimizing the Projection Index
Visualizing Projections Using Dynamic Graphics
Software Packages
Bibliographical Notes
Exercises
Linear Discriminant Analysis
Introduction
Example: Wisconsin Diagnostic Breast Cancer Data
Classes and Features
Binary Classification
Bayes's Rule Classifier
Gaussian Linear Discriminant Analysis
LDA via Multiple Regression
Variable Selection
Logistic Discrimination
Gaussian LDA or Logistic Discrimination?
Quadratic Discriminant Analysis
Examples of Binary Misclassification Rates
Multiclass LDA
Bayes's Rule Classifier
Multiclass Logistic Discrimination
LDA via Reduced-Rank Regression
Example: Gilgaied Soil
Examples of Multiclass Misclassification Rates
Software Packages
Bibliographical Notes
Exercises
Recursive Partitioning and Tree-Based Methods
Introduction
Classification Trees
Example: Cleveland Heart-Disease Data
Tree-Growing Procedure
Splitting Strategies
Example: Pima Indians Diabetes Study
Estimating the Misclassification Rate
Pruning the Tree
Choosing the Best Pruned Subtree
Example: Vehicle Silhouettes
Regression Trees
The Terminal-Node Value
Splitting Strategy
Pruning the Tree
Selecting the Best Pruned Subtree
Example: 1992 Major League Baseball Salaries
Extensions and Adjustments
Multivariate Responses
Survival Trees
MARS
Missing Data
Software Packages
Bibliographical Notes
Exercises
Artificial Neural Networks
Introduction
The Brain as a Neural Network
The McCulloch-Pitts Neuron
Hebbian Learning Theory
Single-Layer Perceptrons
Feedforward Single-Layer Networks
Activation Functions
Rosenblatt's Single-Unit Perceptron
The Perceptron Learning Rule
Perceptron Convergence Theorem
Limitations of the Perceptron
Artificial Intelligence and Expert Systems
Multilayer Perceptrons
Network Architecture
A Single Hidden Layer
ANNs Can Approximate Continuous Functions
More than One Hidden Layer
Optimality Criteria
The Backpropagation of Errors Algorithm
Convergence and Stopping
Network Design Considerations
Learning Modes
Input Scaling
How Many Hidden Nodes and Layers?
Initializing the Weights
Overfitting and Network Pruning
Example: Detecting Hidden Messages in Digital Images
Examples of Fitting Neural Networks
Related Statistical Methods
Projection Pursuit Regression
Generalized Additive Models
Bayesian Learning for ANN Models
Laplace's Method
Markov Chain Monte Carlo Methods
Software Packages
Bibliographical Notes
Exercises
Support Vector Machines
Introduction
Linear Support Vector Machines
The Linearly Separable Case
The Linearly Nonseparable Case
Nonlinear Support Vector Machines
Nonlinear Transformations
The ""Kernel Trick""
Kernels and Their Properties
Examples of Kernels
Optimizing in Feature Space
Grid Search for Parameters
Example: E-mail or Spam?
Binary Classification Examples
SVM as a Regularization Method
Multiclass Support Vector Machines
Multiclass SVM as a Series of Binary Problems
A True Multiclass SVM
Support Vector Regression
e-Insensitive Loss Functions
Optimization for Linear ϵ-Insensitive Loss
Extensions
Optimization Algorithms for SVMs
Software Packages
Bibliographical Notes
Exercises
Cluster Analysis
Introduction
What Is a Cluster?
Example: Old Faithful Geyser Eruptions
Clustering Tasks
Hierarchical Clustering
Dendrogram
Dissimilarity
Agglomerative Nesting (agnes)
A Worked Example
Divisive Analysis (diana)
Example: Primate Scapular Shapes
Nonhierarchical or Partitioning Methods
i-Means Clustering (kmeans)
Partitioning Around Medoids (pam)
Fuzzy Analysis (fanny)
Silhouette Plot
Example: Landsat Satellite Image Data
Self-Organizing Maps (SOMs)
The SOM Algorithm
On-line Versions
Batch Version
Unified Distance Matrix
Component Planes
Clustering Variables
Gene Clustering
Principal Component Gene Shaving
Example: Colon Cancer Data
Block Clustering
Two Way Clustering of Microarray Data
Biclustering
Plaid Models
Example: Leukemia (ALL/AML) Data
Clustering Based Upon Mixture Models
The EM Algorithm for Finite Mixtures
How Many Components?
Software Packages
Bibliographical Notes
Exercises
Multidimensional Scaling and Distance Geometry
Introduction
Example: Airline Distances
Two Golden Oldies
Example: Perceptions of Color in Human Vision
Example: Confusion of Morse Code Signals
Proximity Matrices
Comparing Protein Sequences
Optimal Sequence Alignment
Example: Two Hemoglobin Chains
String Matching
Edit Distance
Example: Employee Careers at Lloyds Bank
Classical Scaling and Distance Geometry
From Dissimilarities to Principal Coordinates
Assessing Dimensionality
Example: Airline Distances (Continued)
Example: Mapping the Protein Universe
Distance Scaling
Metric Distance Scaling
Metric Least-Squares Scaling
Sammon Mapping
Example: Lloyds Bank Employees
Bayesian MDS
Nonmetric Distance Scaling
Disparities
The Stress Function
Fitting Nonmetric Distance-Scaling Models
How Good Is an MDS Solution?
How Many Dimensions?
Software Packages
Bibliographical Notes
Exercises
Committee Machines
Introduction
Bagging
Bagging Tree-Based Classifiers
Bagging Regression-Tree Predictors
Boosting
AdaBoost: Boosting by Reweighting
Example: Aqueous Solubility in Drug Discovery
Convergence Issues and Overfitting
Classification Margins
AdaBoost and Maximal Margins
A Statistical Interpretation of AdaBoost
Some Questions About AdaBoost
Gradient Boosting for Regression
Other Loss Functions
Regularization
Noisy Class Labels
Random Forests
Randomizing Tree Construction
Generalization Error
An Upper Bound on Generalization Error
Example: Diagnostic Classification of Four Childhood Tumors
Assessing Variable Importance
Proximities for Classical Scaling
Identifying Multivariate Outliers
Treating Unbalanced Classes
Software Packages
Bibliographical Notes
Exercises
Latent Variable Models for Blind Source Separation
Introduction
Blind Source Separation and the Cocktail-Party Problem
Independent Component Analysis
Applications of ICA
Example: Cutaneous Potential Recordings of a Pregnant Woman
Connection to Projection Pursuit
Centering and Sphering
The General ICA Problem
Linear Mixing: Noiseless ICA
Identifiability Aspects
Objective Functions
Nonpolynomial-Based Approximations
Mutual Information
The FastICA Algorithm
Example: Identifying Artifacts in MEG Recordings
Maximum-Likelihood ICA
Kernel ICA
Exploratory Factor Analysis
The Factor Analysis Model
Principal Components FA
Maximum-Likelihood FA
Example: Twenty-four Psychological Tests
Critiques of MLFA
Confirmatory Factor Analysis
Independent Factor Analysis
Software Packages
Bibliographical Notes
Exercises
Nonlinear Dimensionality Reduction and Manifold Learning
Introduction
Polynomial PCA
Principal Curves and Surfaces
Curves and Curvature
Principal Curves
Projection-Expectation Algorithm
Bias Reduction
Principal Surfaces
Multilayer Autoassociative Neural Networks
Main Features of the Network
Relationship to Principal Curves
Kernel PCA
PCA in Feature Space
Centering in Feature Space
Example: Food Nutrition (Continued)
Kernel PCA and Metric MDS
Nonlinear Manifold Learning
Manifolds
Data on Manifolds
Isomap
Local Linear Embedding
Laplacian Eigenmaps
Hessian Eigenmaps
Other Methods
Relationships to Kernel PCA
Software Packages
Bibliographical Notes
Exercises
Correspondence Analysis
Introduction
Example: Shoplifting in The Netherlands
Simple Correspondence Analysis
Two-Way Contingency Tables
Row and Column Dummy Variables
Example: Hair Color and Eye Color
Profiles, Masses, and Centroids
Chi-squared Distances
Total Inertia and Its Decomposition
Principal Coordinates for Row and Column Profiles
Graphical Displays
Square Asymmetric Contingency Tables
Example: Occupational Mobility in England
Multiple Correspondence Analysis
The Multivariate Indicator Matrix
The Burt Matrix
Equivalence and an Implication
Example: Satisfaction with Housing Conditions
A Weighted Least-Squares Approach
Software Packages
Bibliographical Notes
Exercises
References
Index of Examples
Author Index
Subject Index

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